## A Course of Mathematics: For the Use of Academies as Well as Private Tuition : in Two Volumes, Volume 2W. E. Dean, 1831 |

### From inside the book

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**Hence**we may immediately deduce a very important theo . rem : for , the first of these equations , divided by the second , gives sin . A Sii . B = + , and the first divided by the third gives C sin . A sin . c ; whence since two equal ... Page 20

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**Hence**, substituting I for Rand 3 for cos a , in the ex- pression sin A = √ ( 2R2 + 2R COSA ) ... ( equa . XII ) , it becomes sin 15 ° = ( 2-3 ) = 2588190 .**Hence**, sin 75 ° = cos15 ° = √ [ 1- ( 2-3 ) ] = √ ( 2 + 3 ) = < + √2 4 ... Page 23

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**Hence**the process is this : From tan a + tan B + tan c = 5-3047057 Take tan attan B. Remains tan c = 3-1601988 = 2-1445069 = tan 65 ° . From tan a + tan B + tan c = 5-3047057 Take tan B + tanc ... Remains tan a . = 3-8765577 = 1.4281480 ... Page 27

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**Hence**it follows , that the surface of a spherical triangle BAC , and the three planes which determine it , form a kind of triangular pyramid , BCGA , of which the vertex & is at the centre of the sphere , the base ABC a portion of the ... Page 38

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**Hence**it may be deduced , that each solid angle of a regu . lar prism , with triangular base , is half each solid angle of a prism with a regular hexagonal base . Each with regular square base = of each , with regular octagonal base ...### Other editions - View all

### Common terms and phrases

abscissas altitude axis ball base beam becomes body centre of gravity circle conic surface consequently Corol cosine curve cylinder denote density descending determine diameter direction distance draw earth equa equal equation equilibrio EXAM expression feet find the fluent fluid force given fluxion given plane ground line Hence horizontal plane hyperbola inches inclined plane intersection length logarithm measure motion moving multiplied nearly ordinates parabola parallel pendulum perpendicular position pressure prob PROBLEM PROP proportional quantity radius ratio rectangle resistance right angles right line roots Scholium side sine solid angle space specific gravity spherical excess spherical triangle square straight line supposed surface tangent theorem theref tion velocity vertex vertical plane vertical projections vibrations weight whole

### Popular passages

Page 467 - Or, by an. 249 of the same, the pressure is equal to the weight of a column of the fluid...

Page 74 - To prove that the exterior angle of a triangle is equal to the sum of the two interior opposite angles (see fig.

Page 203 - VI, its Corollaries and Scholium, for Constant Forces, are true in the Motions of. Bodies freely descending by their own Gravity ; namely, that the Velocities are as the Times, and the Spaces as the Squares of the Times, or as the Squares of the Velocities. FOR, since the force of gravity is uniform, and constantly the same, at all places near the earth's surface, or at nearly the same distance from the centre of the earth ; and since • this is the force by which bodies descend to the surface ;...

Page 247 - BPC) ; or, the pressure of a fluid on any surface is equal to the weight of a column of the fluid...

Page 297 - The workmen thought that substituting part silver was only a proper <perquisite; which taking air, Archimedes was appointed to examine it ; who, on putting...

Page 35 - Two planes are said to have the same or a like inclination to one another which two other planes have, when the said angles of inclination are equal to one another.

Page 83 - Let a, b, c, be the sides, and A, B, c, the angles of a spherical triangle, on the surface of a sphere whose radius is r ; then...

Page 393 - Multiply the number in the table of multiplicands, by the breadth and square of the depth, both in inches, and divide that product by the length, also, in inches; the quotient will be the weight in Jbs.t Example 1.

Page 252 - Weigh the denser body and the compound mass, separately, both in water and out of it ; then find how much each loses in water, by subtracting its weight in water from its weight in air ; and subtract the less of these remainders from the greater. Then...

Page 148 - Body is either Hard, Soft, or Elastic. A Hard Body is that whose parts do not yield to any stroke or percussion, but retains its figure unaltered. A Soft Body is that whose parts yield^to any stroke or impression, without restoring themselves again ; the figure of the body remaining altered.